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Physical Review Letters

Microwave Transitions in Pairs of Rb Rydberg Atoms

Yinan Yu, Hyunwook Park, Thomas F. Gallagher

Published Oct 22, 2013• 18 citations
Publisher

Abstract

We have observed microwave transitions between pairs of cold Rb atoms, specifically, transitions between the molecular nd(5/2)nd(5/2) and (n+1)d(j)(n-2)f states for 41≤n≤44. (We use the separated atom limits as labels.) The transition is allowed because the dipole-dipole induced configuration interaction between the nd(5/2)nd(5/2) state and the energetically close (n+2)p(3/2)(n-2)f state leads to an admixture of the latter into the former. Such transitions may provide a way of selecting closely spaced pairs of atoms.

DOI
10.1103/physrevlett.111.173001

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Microwave transitions from pairs of Rb nd5/2nd5/2 atoms

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We have observed resonant microwave transitions between pairs of atoms. Specifically, we have observed the processes $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2){f}_{7/2}$ and $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+2){p}_{3/2}(n\ensuremath{-}1){d}_{5/2}$ for $35\ensuremath{\le}n\ensuremath{\le}44$. These transitions are allowed due to the dipole-dipole-induced configuration interaction between the $n{d}_{5/2}n{d}_{5/2}$ state and the energetically nearby $(n+2){p}_{3/2}(n\ensuremath{-}2){f}_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\ensuremath{\le}n\ensuremath{\le}42$. Over this range of $n$ the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.

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MICROWAVE TRANSITIONS BETWEEN PAIR STATES COMPOSED OF TWO Rb RYDBERG ATOMS

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Microwave transitions between pair states composed of two Rb Rydberg atoms in a magneto-optical trap are investigated. Our current interest is the transition from ndnd to (n+1)d(n-2)f states. This transition is allowed because the dipole-dipole induced configuration interaction between the ndnd state and the energetically close (n+2)p(n-2)f state admixes some of the latter state into the former. The resonance frequencies of the ndnd-(n+1)d(n-2)f transitions for n=35 to 42 have been measured and found to agree well with the calculated values. In addition, the power shifts of the resonance frequencies have been measured for n=35 to 42. The dependence of the fractional population transfer from the ndnd to (n+1)d(n-2)f states on the microwave field strength and atomic density has been measured and can be compared to a simple theoretical model. This work has been supported by the Air Force Office of Scientific Research.

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Microwave Transitions of Cold Rydberg Atom Pairs

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This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.

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Microwave pump-probe experiments starting with a cold gas of Rb $34s$ atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.

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Microwave transitions of pairs of cold Rb Rydberg atoms as Forster resonances of Floquet states

Jeonghun Lee, Javed Iqbal, Thomas F. Gallagher

Previous measurements of single photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f$ transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the $n{d}_{5/2}n{d}_{5/2}$ and the nearly degenerate $(n+2){p}_{3/2}(n\ensuremath{-}2)f$ states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f$, two photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f$, and three photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f$ microwave transitions. We show that both single and multiphoton microwave transitions are conveniently described as Forster resonant energy transfers between resonant Floquet states, and we show that the Floquet-Forster model reduces to the CI model used previously. Finally, to show that the transitions observed previously are by no means unique, we report pair transitions with different initial and final states as well as radio instead of microwave frequencies.

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Dipole-dipole broadening of Rb ns−np microwave transitions

Hyunwook Park, Paul J. Tanner, Brigitte J. C. Claessens +2 more

The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as ${n}^{2}$, a broadening rate scaling as ${n}^{4}$ is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm${}^{3}$ is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the $np$ atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.

Physical Review A•Aug 5, 2011•40 citations
We have observed microwave transitions between pairs of cold Rb atoms, specifically, transitions between the molecular nd(5/2)nd(5/2) and (n+1)d(j)(n-2)f states for 41≤n≤44. (We use the separated atom limits as labels.) The transition is allowed because the dipole-dipole induced configuration interaction between the nd(5/2)nd(5/2) state and the energetically close (n+2)p(3/2)(n-2)f state leads to an admixture of the latter into the former. Such transitions may provide a way of selecting closely spaced pairs of atoms.
We have observed resonant microwave transitions between pairs of atoms. Specifically, we have observed the processes $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2){f}_{7/2}$ and $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+2){p}_{3/2}(n\ensuremath{-}1){d}_{5/2}$ for $35\ensuremath{\le}n\ensuremath{\le}44$. These transitions are allowed due to the dipole-dipole-induced configuration interaction between the nd5/2nd5/2n{d}_{5/2}n{d}_{5/2}nd5/2​nd5/2​ state and the energetically nearby $(n+2){p}_{3/2}(n\ensuremath{-}2){f}_{7/2}$ state, which admixes some of the latter into the former. The resulting microwave transitions are analogous to two-photon transitions in which one of the photons has been replaced by the dipole-dipole interaction. We have developed a configuration interaction description of the transitions, which gives a good description of the interaction over the range $35\ensuremath{\le}n\ensuremath{\le}42$. Over this range of nnn the detuning varies from 0.095 to 1.482 GHz, the microwave frequencies vary from 26.970 to 45.916 GHz, and the requisite microwave powers vary by a factor of over 1000.
Microwave transitions between pair states composed of two Rb Rydberg atoms in a magneto-optical trap are investigated. Our current interest is the transition from ndnd to (n+1)d(n-2)f states. This transition is allowed because the dipole-dipole induced configuration interaction between the ndnd state and the energetically close (n+2)p(n-2)f state admixes some of the latter state into the former. The resonance frequencies of the ndnd-(n+1)d(n-2)f transitions for n=35 to 42 have been measured and found to agree well with the calculated values. In addition, the power shifts of the resonance frequencies have been measured for n=35 to 42. The dependence of the fractional population transfer from the ndnd to (n+1)d(n-2)f states on the microwave field strength and atomic density has been measured and can be compared to a simple theoretical model. This work has been supported by the Air Force Office of Scientific Research.
This dissertation consists of three microwave spectroscopy experiments performed with cold Rb Rydberg atoms in Magneto Optical Trap.The first experiment is a systematic study of a particular type of transition which was first observed in 2012 that involves a pair of Rydberg atoms.In this transition, even though only one microwave photon is absorbed, both atoms in the pair change states.In particular, we describe the transition with the configuration interaction (CI) model and experimentally verify the scaling of fractional population transfer predicted by the CI model.The second experiment builds on the first experiment and reports observations of additional single and multi photon microwave transitions that are allowed due to the same CI as in the first experiment.The observations show clearly that this type of transition involving a pair of Rydberg atoms are a lot more common than initially thought.We show that the transitions can be conveniently described as Forster resonances of Floquet states.The last experiment reports on the technique we used to measure the ng and nh series quantum defects and the ionic dipole and quadrupole polarizabilities of 85 Rb.The technique allows us to obtain zero field intervals of (n + 1)d 5/2 → ng and (n + 1)d 5/2 → nh intervals despite the fact that we can only control the stray electric field in one direction.Using the technique, the quantum defects of ng and nh were determined to be 0.0039741(16) and 0.0014066(57), respectively.The ionic II dipole and quadrupole polarizabilities were determined to be 9.12(2)a 3 0 and 14(3)a 5 0 , respectively.
Microwave pump-probe experiments starting with a cold gas of Rb 34s34s34s atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.
Previous measurements of single photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+1){d}_{j}(n\ensuremath{-}2)f$ transitions by two of us were described as microwave transitions made possible by configuration interaction (CI) between the nd5/2nd5/2n{d}_{5/2}n{d}_{5/2}nd5/2​nd5/2​ and the nearly degenerate $(n+2){p}_{3/2}(n\ensuremath{-}2)f$ states [Lee and Gallagher, Phys. Rev. A 93, 062509 (2016)]. Here we report the observation of the one photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){s}_{1/2}(n\ensuremath{-}2)f$, two photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+3){p}_{j}(n\ensuremath{-}2)f$, and three photon $n{d}_{5/2}n{d}_{5/2}\ensuremath{\rightarrow}(n+4){s}_{1/2}(n\ensuremath{-}2)f$ microwave transitions. We show that both single and multiphoton microwave transitions are conveniently described as Forster resonant energy transfers between resonant Floquet states, and we show that the Floquet-Forster model reduces to the CI model used previously. Finally, to show that the transitions observed previously are by no means unique, we report pair transitions with different initial and final states as well as radio instead of microwave frequencies.
The dipole-dipole broadening of $ns\ensuremath{-}np$ microwave transitions of cold Rb Rydberg atoms in a magneto-optical trap has been recorded for $28\ensuremath{\leqslant}n\ensuremath{\leqslant}51$. Since the electric dipole transition matrix elements scale as n2{n}^{2}n2, a broadening rate scaling as n4{n}^{4}n4 is expected and a broadening rate of $8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}{n}^{4}$ MHz cm3{}^{3}3 is observed. The observed broadening is smaller than expected from a classical picture due to the spin-orbit interaction in the npnpnp atoms. The broadened resonances are asymmetric and cusp shaped, and their line shapes can be reproduced by a diatomic model which takes into account the dipole-dipole interaction, including the spin-orbit interaction, the strengths of the allowed microwave transitions, and the distribution of the atomic spacings in the trap.